Question

The following data gives the information of life of 200 electric bulbs (in hours) as follows,Find the modal life of the electric bulbs.
Life in hours
0-20
20-40
40-60
60-80
80-100
100-120

Number of electric bulbs
26
31
35
42
82
71

Answer 1

Dear Student,

Answer: Mode = 95.68 hours

Solution:

As we know that mode is the highest frequency data, but it is easy to detect easily in ungrouped data.

when it comes to the grouped data Mode is calculated from the formula

Mode = $l + h (\frac{f_{1} - f_{0}}{2f_{1}-f_{0}-f_{2}} )$

Modal class = higher frequency class ( 80 -100)

here l = lower limit of model class = 80

h = size of model class = 20

f1 = frequency of modal class = 82

f0 = frequency of preceding class = 42

f2 = frequency of proceeding class = 71

Mode = $80 + 20 (\frac{82 - 42}{2×82-42-71} )$

Mode = $80 + 20 (\frac{40}{51} )$

= 80 + 800/51

= 80 + 15.68

Mode = 95.68 hours

Hope it helps you.